Six states held primaries on Tuesday, and once again anti-establishment candidates came up short in high-profile Republican showdowns.

That's a sharp difference with what we have seen over the last two election cycles, when establishment Republicans were overwhelmed by the insurgency in their own party and did little to stop it. But they appear to have turned the tables on the conservatives so far in this election cycle and have a string of victories to show for it.

Here are five things we learned Tuesday night:

1. Establishment GOPhas learned to play ball: Since its birth in 2009, the tea party has had successes in primaries but those have given the GOP plenty of headaches and hurt its chances of winning back the Senate, effectively costing Republicans five winnable elections over the last two cycles.

This year, the establishment has had the upper hand in most contests against tea party-backed challengers. Showdowns on Tuesday in Kentucky, Idaho, Georgia, and Oregon kept that winning streak going.

In Kentucky, Senate Minority Leader Mitch McConnell easily dispatched Matt Bevin, who enjoyed the support of tea party activists and anti-establishment groups. It was a similar story in Idaho, where eight-term Rep. Mike Simpson also beat back a similar challenge from the right.

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In Georgia's free-for-all Republican Senate primary, the two finishers who now move onto a July runoff were considered the most acceptable to the establishment. And in Oregon, pediatric neurosurgeon Dr. Monica Wehby, who enjoyed support from the GOP establishment, defeated a more conservative candidate for the state's Republican Senate nomination.

How did they do it?

The winners all ran smart campaigns and were fortunate that the losers stumbled. And outside help also made a difference. The pro-business U.S. Chamber of Commerce spent more than $4 million to support McConnell, Simpson and Rep. Jack Kingston, who will face off with businessman David Perdue in the Georgia runoff.

One reason for the winning streak: The establishment has learned how to play ball with the tea party.

"Every establishment candidate ran like a tea party candidate. It's hard to tell the difference this time around, because they had a uniting factor in opposing Obamacare but also united on issues like immigration and trade and climate change. The establishment Republican Party ran to the right this time," said CNN Chief Political Analyst Gloria Borger.

While Democrats argue that the move to the right will backfire on the GOP come November, midterm elections are traditionally low turnout affairs compared to presidential elections. And in such contests, the key to victory is often getting out the base.

2. Is Rand Paul now all in for McConnell?: Sen. Rand Paul endorsed McConnell in the primary, but his support seemed tepid at best. In February, Paul said he backed his fellow Kentucky senator simply "because he asked me."

His lukewarm support wasn't all that surprising. After all, McConnell didn't back Paul in the GOP primary in 2010, though he made amends and endorsed Paul in the general election.

Paul hasn't been McConnell's most vocal surrogate, but on Tuesday night he delivered an enthusiastic video message at McConnell's election night headquarters, preaching his theme of party unity, and couching his support for McConnell as a chance to help Republicans take the Senate.

"Four years ago, after a contentious primary, Sen. McConnell pulled the party together. Republicans united to forge a big victory and allow me to be a U.S. senator. Republicans must now come together again. We must unite to stop Harry Reid and his liberal allies from controlling the Senate," he said.

3. Putting down the swords: Speaking of unity, Paul wasn't the only one calling for a more cohesive GOP.

Conservatives seemed to be keenly aware Tuesday night that McConnell is heading into a tight race against Democrat Alison Lundergan Grimes. Despite disagreeing with the longtime senator on some big issues, a number of conservative groups were quick to offer an olive branch and call for unity after Bevin lost to McConnell.

They made it clear that potentially losing Kentucky's Senate seat to a Democrat is much worse than losing it to an establishment Republican.

The Senate Conservatives Fund, which spent big bucks for Bevin, congratulated McConnell in a statement and said, "it's time for Republicans to unite for victory in November."

Erick Erickson, the editor of the influential conservative website RedState, announced Tuesday before the results were in that he "proudly" supported McConnell and sent his campaign $250 to help with the general election.

"People tell me I'm a leader in the conservative movement. Sometimes leading means going where I'd prefer not to," he wrote.

The Madison Project, another group that backed Bevin, also asked "all Republicans to come together to defeat" Grimes.

And in his concession speech, Bevin didn't back McConnell, but he said he has no intention "of supporting the Democratic platform over the Republican platform."

But not everyone was singing quite the same tune. The group FreedomWorks, which plays a major role in the tea party movement, didn't call for Republicans to unite around McConnell, but they didn't attack him either.

"Competition always breeds stronger candidates, and there is an improved conservative candidate heading into the general election as a result," the group's president, Matt Kibbe, said in a statement.

The questions is: Will conservatives be ready to hold hands with the establishment every time their candidate loses? Or is this simply a strategic alliance to boost the chances of a GOP win in November?

4. Clinton support is no guarantee: Marjorie Margolies, a former congresswoman from Pennsylvania who was seeking a comeback, lost Tuesday night in a Democratic House primary, despite having support from some of the most popular Democrats in the country: Bill and Hillary Clinton.

They also happen to be Margolies' in-laws. Her son, Marc Mezvinsky, married Chelsea Clinton in 2010, and the couple are expecting their first child this fall.

Their support for Margolies was by far the Clintons' most visible campaign activity this year. But Tuesday night's race, which went to Brendan Boyle, indicated that support from the Clintons isn't necessarily a golden ticket.

Margolies represented the eastern Pennsylvania seat for two years in the early '90s. She ended up losing her seat after being the deciding vote in favor of Clinton's budget.

Bill Clinton didn't forget the price she paid. He campaigned for Margolies in April and noted that he "would be here if her son was not my son-in-law."

Margolies told Borger that she knew it was a risky move to have the Clintons publicly supporting her.

"We always knew that if they came in too much, we would be blamed for their coming in too much. If they don't come in enough, then people would say they didn't come in enough. You're kind of damned if you do, damned if you don't," Margolies said. "They have done everything we've asked them to do, and I am running on what I have accomplished in the last 20 years and not on my affiliation with the Clintons."

5. What happens in May matters in November: We already knew this, but it's worth repeating: Primary results have major consequences.

The victories by McConnell in Kentucky, and Wehby in Oregon, and with Perdue and Kingston advancing to the runoff in the Georgia Senate race ahead of three more conservative candidates, the GOP improved its chances come November.

By nominating candidates who have a better shot of appealing to the wider electorate that votes in November, Republicans now upped their odds when it comes to winning the six Democratic-held seats the party needs to win back the control of the Senate.

The victories on Tuesday followed establishment Senate primary wins in North Carolina two weeks ago and in Texas in March.

With establishment candidates in most of the remaining primaries leading in the public opinion polls, the trend should continue.